When we write the equation of the line, we write it in slope-intercept form.
What is slope-intercept form?
Slope-intercept form is the "formula" we use to write the equation of a line. It looks like this: y = mx + b
Each part of the equation has a specific meaning. The "m" represents the slope of the line. The "b" represents the y-intercept of the line. The "x" and "y" represent the coordinates of any point on the line (x,y).
When we write an equation out in slope-intercept form, we need to substitute numbers in for "m" (the slope) and "b" (the y-intercept). This is why this form is called slope - intercept form. The "x" and "y" will stay as variables. For example:
y = 3x + 7
y = (-1/2)x - 4
TASK: What two things do we need to have in order to write the equation of a line in slope-intercept form?
How do we write equations in slope-intercept form?
There are three different scenarios on the Regents in which you will be asked to write an equation in slope-intercept form. In this lesson, we will talk about two of those situations:
1. When you're given the slope and the y-intercept
2. When you're given the slope and another point on the line (not the y-intercept)
When you're given the slope and the y-intercept:
Since the only two things we need to know to write the equation of the line in slope-intercept form are the slope and the y-intercept, if they're both given to you, you can SUBSTITUTE them into the equation y = mx + b
For example: Write the equation in slope-intercept form of the line that has a slope of -2 and a y-intercept of 7.
Based on what's given in the problem, we know that m = -2 and b = 7. Therefore, we can substitute them into y = mx + b and we get: y = -2x + 7.
When you're given the slope and another point on the line:
Example: Find the equation of the line that has a slope of 2/3 and goes through the point (-3,1)
The two things we need to write the equation of a line in slope-intercept form are the SLOPE and the Y-INTERCEPT. One of these things (the slope) is given to us in this problem. Then, we need to use the other information given in the problem to find the y-intercept.
So far, we know that m = 2/3. We need to find "b." The other information given (-3,1) is another point on the line and we can substitute them in for "x" and "y." We get:
y = (2/3)x + b --> Substitute 2/3 in for "m"
1 = (2/3)(-3) + b --> Substitute 1 in for "y" and -3 in for "x". These numbers come from the (x,y) from the point given (-3,1).
1 = -2 + b --> Simplify by multiplying 2/3 and -3
3 = b --> Simplify by adding 2 on both sides
Now we know what "b" is and what "m" is. m = 2/3 and b = 3. Using this information, we can write the equation of the line and we get:
y = (2/3)x + 3
Note: If "b" is a negative number, we would write -- instead of + in the equation.
TASK: Complete the four practice Regents problems below. Please SHOW ALL YOUR WORK.**
What is slope-intercept form?
Slope-intercept form is the "formula" we use to write the equation of a line. It looks like this: y = mx + b
Each part of the equation has a specific meaning. The "m" represents the slope of the line. The "b" represents the y-intercept of the line. The "x" and "y" represent the coordinates of any point on the line (x,y).
When we write an equation out in slope-intercept form, we need to substitute numbers in for "m" (the slope) and "b" (the y-intercept). This is why this form is called slope - intercept form. The "x" and "y" will stay as variables. For example:
y = 3x + 7
y = (-1/2)x - 4
TASK: What two things do we need to have in order to write the equation of a line in slope-intercept form?
How do we write equations in slope-intercept form?
There are three different scenarios on the Regents in which you will be asked to write an equation in slope-intercept form. In this lesson, we will talk about two of those situations:
1. When you're given the slope and the y-intercept
2. When you're given the slope and another point on the line (not the y-intercept)
When you're given the slope and the y-intercept:
Since the only two things we need to know to write the equation of the line in slope-intercept form are the slope and the y-intercept, if they're both given to you, you can SUBSTITUTE them into the equation y = mx + b
For example: Write the equation in slope-intercept form of the line that has a slope of -2 and a y-intercept of 7.
Based on what's given in the problem, we know that m = -2 and b = 7. Therefore, we can substitute them into y = mx + b and we get: y = -2x + 7.
When you're given the slope and another point on the line:
Example: Find the equation of the line that has a slope of 2/3 and goes through the point (-3,1)
The two things we need to write the equation of a line in slope-intercept form are the SLOPE and the Y-INTERCEPT. One of these things (the slope) is given to us in this problem. Then, we need to use the other information given in the problem to find the y-intercept.
So far, we know that m = 2/3. We need to find "b." The other information given (-3,1) is another point on the line and we can substitute them in for "x" and "y." We get:
y = (2/3)x + b --> Substitute 2/3 in for "m"
1 = (2/3)(-3) + b --> Substitute 1 in for "y" and -3 in for "x". These numbers come from the (x,y) from the point given (-3,1).
1 = -2 + b --> Simplify by multiplying 2/3 and -3
3 = b --> Simplify by adding 2 on both sides
Now we know what "b" is and what "m" is. m = 2/3 and b = 3. Using this information, we can write the equation of the line and we get:
y = (2/3)x + 3
Note: If "b" is a negative number, we would write -- instead of + in the equation.
TASK: Complete the four practice Regents problems below. Please SHOW ALL YOUR WORK.**
1.
2.
3.
4.